Step 1: categorization.
For employing \({\mathsf {SIT}}\) , the first step is partitioning candidate groups for each target user, i.e., the categorization stage.
To explore the group information for the source-target pair,
given a graph \(\mathcal {G} =(\mathcal {E})\)  and a target user \(v_t\) , we partition the source neighborhood of \(v_t\)  based on the weakly connected components (see Definition REF ).
Specifically, following operations in [1]}, [2]}, [3]}, [4]}, we first extract each weakly connected component (dubbed as \({\mathsf {CC}}\) ) from the ego network \(\mathcal {G} _t = (\mathcal {N} _t,\mathcal {R} _t)\)  of \(v_t\) , and then call all sources in a given \({\mathsf {CC}}\)  and the target \(v_t\)  as a candidate group \(\mathcal {C} \) , since \(v_t\)  connects to all sources in the \({\mathsf {CC}}\)  by edges in \(\mathcal {E} _{t}\) . To exemplify, given an input graph as shown in Figure REF (a), the source neighborhood of target node \(v_1\)  is partitioned into two candidate groups (shaded in two colors in Figure REF (b)), among which the group \(\mathcal {C} \)  is constituted by \(v_1,v_2,v_3,v_4\) .
The rationale for employing \({\mathsf {CC}}\)  is two-fold. First, as suggested in \({\mathsf {SIT}}\)   [5]}, the candidate group requires to be categorized in a more general way to mitigate the in-group bias. For instance, employers in two departments of the same company should be categorized into one company group rather than split into two department groups.
By definition, the \({\mathsf {CC}}\)  can satisfy this requirement, as the inside nodes of two \({\mathsf {CCs}}\)  are isolated (i.e., no path).
Second, \({\mathsf {CC}}\)  is a simple but effective way to represent the community in the ego network of a user [4]}, [7]}. As evidence, [4]} finds that employing \({\mathsf {CCs}}\)  for the link prediction can achieve comparable or even slightly better performance than employing communities detected by the state-of-the-art methods.
